Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
10th Edition
ISBN: 9781285464640
Author: Soo T. Tan
Publisher: Brooks Cole
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Textbook Question
Chapter 5.6, Problem 19E
Demand For Computers Universal Instruments found that the monthly demand for its new line of Galaxy Home Computers t months after the line was placed on the market was given by
D(t) = 2000 − 1500e−0.05t (t > 0)
Graph this function and answer the following questions:
- a. What is the demand after 1 month? After 1 year? After 2 years? After 5 years?
- b. At what level is the demand expected to stabilize?
- c. Find the rate of growth of the demand after the tenth month.
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Chapter 5 Solutions
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Ch. 5.1 - Define the exponential function f with base b and...Ch. 5.1 - For the exponential function y = bx (b 0, b 1),...Ch. 5.1 - a. 43 45 b. 33 36Ch. 5.1 - a. (21)3 b. (32)3Ch. 5.1 - a. 9(9)1/2 b. 5(5)1/2Ch. 5.1 - a. [(12)3]2 b. [(13)2]3Ch. 5.1 - a. (3)4(3)5(3)8 b. (24)(25)21Ch. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - a. (116)1/4(2764)1/3 b. (827)1/3(81256)1/4
Ch. 5.1 - a. (64x9)1/3 b. (25x3y4)1/2Ch. 5.1 - Prob. 10ECh. 5.1 - a. 6a43a3 b. 4b412b6Ch. 5.1 - a. y3/2y5/3 b. x3/5x8/3Ch. 5.1 - a. (2x3y2)3 b. (4x2y2z3)2Ch. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - In Exercises 17-26. solve the equation for x 17....Ch. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - In Exercises 17-26. solve the equation for x 22....Ch. 5.1 - In Exercises 17-26, solve the equation for x 23....Ch. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - In Exercises 27-36, sketch the graphs of the given...Ch. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - In Exercises 27-36, sketch the graphs of the given...Ch. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - A function f has the former f(x) = Aekx. Find f if...Ch. 5.1 - If f(x) = Axekx, find f(3) if f(1) = 5 and f(2) =...Ch. 5.1 - If f(t)=10001+Bekt find f(5) given that f(0) = 20...Ch. 5.1 - Decline of American Idol After having been on the...Ch. 5.1 - Renewable Energy Developing countries are...Ch. 5.1 - Online Shoppers According to a study conducted by...Ch. 5.1 - Internet Users in China The number of Internet...Ch. 5.1 - U.S. Cell Phone Subscribers The number of cell...Ch. 5.1 - Alternative Minimum Tax The alternative minimum...Ch. 5.1 - Absorption of Drugs The concentration of a drug in...Ch. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - In Exercises 49-54, determine whether the...Ch. 5.1 - Prob. 54ECh. 5.1 - Prob. 1TECh. 5.1 - Prob. 2TECh. 5.1 - Prob. 3TECh. 5.1 - Prob. 4TECh. 5.1 - Prob. 5TECh. 5.1 - Plot the graphs of f(x) = (1/2)x, g(x) = (1/3)x,...Ch. 5.1 - Prob. 7TECh. 5.1 - Prob. 8TECh. 5.1 - Prob. 9TECh. 5.1 - Prob. 10TECh. 5.1 - Prob. 11TECh. 5.1 - Prob. 12TECh. 5.1 - Prob. 14TECh. 5.2 - a. Define y = logb x. b. Define the logarithmic...Ch. 5.2 - Prob. 2CQCh. 5.2 - Prob. 3CQCh. 5.2 - Prob. 4CQCh. 5.2 - Prob. 1ECh. 5.2 - Prob. 2ECh. 5.2 - In Exercises 1-10, express each equation in...Ch. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - In Exercises 1-10, express each equation in...Ch. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 - In Exercises 1-10, express each equation in...Ch. 5.2 - In Exercises 11-16, given that log 3 0.4771 and...Ch. 5.2 - In Exercises 11-16, given that log 3 0.4771 and...Ch. 5.2 - In Exercises 11-16, given that log 3 0.4771 and...Ch. 5.2 - In Exercises 11-16, given that log 3 0.4771 and...Ch. 5.2 - In Exercises 11-16, given that log 3 0.4771 and...Ch. 5.2 - In Exercises 11-16, given that log 3 0.4771 and...Ch. 5.2 - In Exercises 17-20, write the expression as the...Ch. 5.2 - In Exercises 17-20, write the expression as the...Ch. 5.2 - In Exercises 17-20, write the expression as the...Ch. 5.2 - In Exercises 17-20, write the expression as the...Ch. 5.2 - In Exercises 21-28, use the laws of logarithms to...Ch. 5.2 - In Exercises 21-28, use the laws of logarithms to...Ch. 5.2 - In Exercises 21-28, use the laws of logarithms to...Ch. 5.2 - In Exercises 21-28, use the laws of logarithms to...Ch. 5.2 - In Exercises 21-28, use the laws of logarithms to...Ch. 5.2 - In Exercises 21-28, use the laws of logarithms to...Ch. 5.2 - In Exercises 21-28, use the laws of logarithms to...Ch. 5.2 - In Exercises 21-28, use the laws of logarithms to...Ch. 5.2 - Prob. 29ECh. 5.2 - In Exercises 29-32, sketch the graph of the...Ch. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - In Exercises 35-44, use logarithms to solve the...Ch. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - In Exercises 35-44, use logarithms to solve the...Ch. 5.2 - In Exercises 35-44, use logarithms to solve the...Ch. 5.2 - In Exercises 35-44, use logarithms to solve the...Ch. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - In Exercises 35-44, use logarithms to solve the...Ch. 5.2 - Prob. 45ECh. 5.2 - Average Life Span One reason for the increase in...Ch. 5.2 - Blood Pressure A normal childs systolic blood...Ch. 5.2 - Magnitude of Earthquakes On the Richter scale, the...Ch. 5.2 - Prob. 49ECh. 5.2 - Barometric Pressure Halleys Law states that the...Ch. 5.2 - Newtons Law of Cooling The temperature of a cup of...Ch. 5.2 - Height of Trees The height (in feet) of a certain...Ch. 5.2 - Obesity Over Time The percentage of obese adults,...Ch. 5.2 - Lengths of Fish The length (in centimeters) of a...Ch. 5.2 - Absorption of Drugs The concentration of a drug in...Ch. 5.2 - Absorption of Drugs The concentration of a drug in...Ch. 5.2 - Forensic SCIENCE Forensic scientists use the...Ch. 5.2 - ELASTICITY OF Demand The demand function for a...Ch. 5.2 - Prob. 59ECh. 5.2 - In Exercises 59-62, determine whether the...Ch. 5.2 - Prob. 61ECh. 5.2 - In Exercises 59-62, determine whether the...Ch. 5.2 - Prob. 63ECh. 5.2 - Prob. 64ECh. 5.2 - a. Given that 2x = ekx, find k. b. Show that, in...Ch. 5.2 - Prob. 66ECh. 5.2 - Prob. 67ECh. 5.2 - Prob. 68ECh. 5.3 - a. What is the difference between simple interest...Ch. 5.3 - Prob. 2CQCh. 5.3 - Prob. 3CQCh. 5.3 - Prob. 4CQCh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - In Exercises 5 and 6, find the effective rate...Ch. 5.3 - Prob. 6ECh. 5.3 - In Exercises 7 and 8, find the present value of...Ch. 5.3 - Prob. 8ECh. 5.3 - Find the accumulated amount after 4 years if 5000...Ch. 5.3 - An amount of 25,000 is deposited in a bank that...Ch. 5.3 - Prob. 11ECh. 5.3 - PRESENT VALUE OF AN INVESTMENT Jada deposited an...Ch. 5.3 - PRESENT VALUE OF AN INVESTMENT How much money...Ch. 5.3 - PRESENT VALUE OF AN INVESTMENT Diego deposited a...Ch. 5.3 - Find the present value of 59,673 due in 5 years at...Ch. 5.3 - Find the interest rate needed for an investment of...Ch. 5.3 - Find the interest rate needed for an investment of...Ch. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - How long will it take 12,000 to grow to 15,000 if...Ch. 5.3 - How long will it take 5000 to grow to 6500 if the...Ch. 5.3 - How long will it take an investment of 2000 to...Ch. 5.3 - How long will it take an investment of 5000 to...Ch. 5.3 - Find the interest rate needed for an investment of...Ch. 5.3 - Find the interest rate needed for an investment of...Ch. 5.3 - How long will it take an investment of 6000 to...Ch. 5.3 - How long will it take an investment of 8000 to...Ch. 5.3 - Prob. 30ECh. 5.3 - Energy Consumption A metropolitan utility company...Ch. 5.3 - Prob. 32ECh. 5.3 - Comparing Investment Returns The value of Marias...Ch. 5.3 - Investments The value of Alans stock portfolio...Ch. 5.3 - Investments The value of Jacks investment...Ch. 5.3 - Investments The value of Arabellas stock portfolio...Ch. 5.3 - Mutual Funds Jodie invested 15,000 in a mutual...Ch. 5.3 - Trust funds A young man is the beneficiary of a...Ch. 5.3 - Retirement Funds Five and a half years ago. Chris...Ch. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Online Retail Sales Online retail sales stood at...Ch. 5.3 - Purchasing Power The year-end inflation rates in...Ch. 5.3 - Saying For College Having received a large...Ch. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Loan Consolidation The proprietors of the Coachmen...Ch. 5.3 - Pensions Eleni, who is now 50 years old, is...Ch. 5.3 - Prob. 49ECh. 5.3 - Real Estate Investments Tower Investments owns a...Ch. 5.3 - Investment Options Investment A offers an 8%...Ch. 5.3 - Investment Returns Zoe purchased a house in 2008...Ch. 5.3 - Investment Returns Julio purchased 1000 shares of...Ch. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Investment Analysis Refer to Exercise 55. Bank A...Ch. 5.3 - Prob. 58ECh. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 1TECh. 5.3 - Prob. 2TECh. 5.3 - Prob. 3TECh. 5.3 - Prob. 4TECh. 5.3 - Prob. 5TECh. 5.3 - Prob. 6TECh. 5.4 - State the rule for differentiating (a) f(x)= ex...Ch. 5.4 - Prob. 2CQCh. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - Prob. 16ECh. 5.4 - Prob. 17ECh. 5.4 - Prob. 18ECh. 5.4 - Prob. 19ECh. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - Prob. 21ECh. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - In Exercises 1-28, find the derivative of the...Ch. 5.4 - Prob. 29ECh. 5.4 - In Exercises 29-32, find the second derivative of...Ch. 5.4 - In Exercises 29-32, find the second derivative of...Ch. 5.4 - In Exercises 29-32, find the second derivative of...Ch. 5.4 - Find an equation of the tangent line to the graph...Ch. 5.4 - Find an equation of the tangent line to the graph...Ch. 5.4 - Determine the intervals where the function...Ch. 5.4 - Determine the intervals where the function f(x) =...Ch. 5.4 - Determine the intervals of concavity for the graph...Ch. 5.4 - Determine the intervals of concavity for the graph...Ch. 5.4 - Find the inflection point of the function f(x) =...Ch. 5.4 - Find the inflection point(s) of the function...Ch. 5.4 - Find the equations of the tangent lines to the...Ch. 5.4 - Find an equation of the tangent line to the graph...Ch. 5.4 - In Exercises 4346, find the absolute extrema of...Ch. 5.4 - Prob. 44ECh. 5.4 - In Exercises 4346, find the absolute extrema of...Ch. 5.4 - Prob. 46ECh. 5.4 - In Exercises 4750, use the curve-sketching...Ch. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - In Exercises 51 and 52, find dy/dx by implicit...Ch. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - In Exercises 53 and 54, find d2y/dx2 by implicit...Ch. 5.4 - Find dy/dx at the point (0, 1) using implicit...Ch. 5.4 - Prob. 56ECh. 5.4 - Online Video Viewers As broadband Internet grows...Ch. 5.4 - Output Per Worker In leading advanced...Ch. 5.4 - Pharmaceutical Theft Pharmaceutical theft has been...Ch. 5.4 - World Population Growth After its fastest rate of...Ch. 5.4 - Sales Promotion The Lady Bug, a womens clothing...Ch. 5.4 - Blood Alcohol Level The percentage of alcohol in a...Ch. 5.4 - Polio Immunization Polio, a once-feared killer,...Ch. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - Marginal Revenue The relationship between the unit...Ch. 5.4 - Prob. 68ECh. 5.4 - Prob. 69ECh. 5.4 - Price Of West The monthly demand for a certain...Ch. 5.4 - Spread of an Epidemic During a flu epidemic, the...Ch. 5.4 - Sales of a Product The total number of units of a...Ch. 5.4 - Elasticity of Demand The quantity demanded each...Ch. 5.4 - Elasticity of Demand Suppose that the demand...Ch. 5.4 - Prob. 75ECh. 5.4 - Prob. 76ECh. 5.4 - Optimal Selling Time Refer to Exercise 49, page...Ch. 5.4 - Maximum Oil Production It has been estimated that...Ch. 5.4 - Blood Alcohol Level Refer to Exercise 62, page...Ch. 5.4 - Prob. 80ECh. 5.4 - Thermometer Readiness A thermometer is moved from...Ch. 5.4 - Diffusion Suppose a cell of volume V is surrounded...Ch. 5.4 - Prob. 83ECh. 5.4 - Prob. 84ECh. 5.4 - Prob. 85ECh. 5.4 - Prob. 86ECh. 5.4 - Prob. 87ECh. 5.4 - Prob. 88ECh. 5.4 - Prob. 89ECh. 5.4 - Prob. 90ECh. 5.4 - Prob. 91ECh. 5.4 - Prob. 92ECh. 5.4 - Prob. 1TECh. 5.4 - Prob. 2TECh. 5.4 - Prob. 3TECh. 5.4 - Prob. 4TECh. 5.4 - Prob. 5TECh. 5.4 - Prob. 6TECh. 5.4 - Prob. 7TECh. 5.4 - Prob. 8TECh. 5.4 - Prob. 9TECh. 5.4 - Increasing Crop Yields If left untreated on bean...Ch. 5.5 - State the rule for differentiating (a) f(x) = In...Ch. 5.5 - Prob. 2CQCh. 5.5 - find the derivative of the function. 1 f(x) = 5 In...Ch. 5.5 - find the derivative of the function. 2 f(x) = ln...Ch. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - find the derivative of the function. 5 f(x) = ln...Ch. 5.5 - Prob. 6ECh. 5.5 - find the derivative of the function. 7 f(x)=lnxCh. 5.5 - Prob. 8ECh. 5.5 - find the derivative of the function. 9 f(x)=ln1x2Ch. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - find the derivative of the function. 12 f(x) = ln...Ch. 5.5 - find the derivative of the function. 13...Ch. 5.5 - Prob. 14ECh. 5.5 - find the derivative of the function. 15 f(x) = x2...Ch. 5.5 - find the derivative of the function. 16 f(x) = 3x2...Ch. 5.5 - find the derivative of the function. 17 f(x)=2lnxxCh. 5.5 - find the derivative of the function. 18...Ch. 5.5 - Prob. 19ECh. 5.5 - find the derivative of the function. 20 f(x) =...Ch. 5.5 - Prob. 21ECh. 5.5 - find the derivative of the function. 22 f(x)=lnx+xCh. 5.5 - find the derivative of the function. 23 f(x) = (ln...Ch. 5.5 - find the derivative of the function. 24 f(x) =...Ch. 5.5 - Prob. 25ECh. 5.5 - find the derivative of the function. 26 f(x)=lnx24Ch. 5.5 - find the derivative of the function. 27 f(x) = ex...Ch. 5.5 - find the derivative of the function. 28...Ch. 5.5 - find the derivative of the function. 29 f(x) = e2t...Ch. 5.5 - find the derivative of the function. 30 g(t) = t2...Ch. 5.5 - find the derivative of the function. 31 f(x)=lnxx2Ch. 5.5 - find the derivative of the function. 32 g(t)=tlntCh. 5.5 - In Exercises 134, find the derivative of the...Ch. 5.5 - In Exercises 134, find the derivative of the...Ch. 5.5 - In Exercises 3540, find the second derivative of...Ch. 5.5 - In Exercises 3540, find the second derivative of...Ch. 5.5 - Prob. 37ECh. 5.5 - In Exercises 3540, find the second derivative of...Ch. 5.5 - In Exercises 3540, find the second derivative of...Ch. 5.5 - In Exercises 3540, find the second derivative of...Ch. 5.5 - In Exercises 4150, use logarithmic differentiation...Ch. 5.5 - Prob. 42ECh. 5.5 - In Exercises 4150, use logarithmic differentiation...Ch. 5.5 - In Exercises 4150, use logarithmic differentiation...Ch. 5.5 - Prob. 45ECh. 5.5 - Prob. 46ECh. 5.5 - In Exercises 4150, use logarithmic differentiation...Ch. 5.5 - In Exercises 4150, use logarithmic differentiation...Ch. 5.5 - Prob. 49ECh. 5.5 - Prob. 50ECh. 5.5 - In Exercises 51 and 52, use implicit...Ch. 5.5 - Prob. 52ECh. 5.5 - Find an equation of the tangent line to the graph...Ch. 5.5 - Find an equation of the tangent line to the graph...Ch. 5.5 - Determine the intervals where the function f(x) =...Ch. 5.5 - Determine the intervals where the function...Ch. 5.5 - Determine the intervals of concavity for the graph...Ch. 5.5 - Prob. 58ECh. 5.5 - Find the inflection points of the function f(x) =...Ch. 5.5 - Find the inflection points of the function f(x) =...Ch. 5.5 - Prob. 61ECh. 5.5 - Prob. 62ECh. 5.5 - Find the absolute extrema of the function f(x) = x...Ch. 5.5 - Prob. 64ECh. 5.5 - In Exercises 65 and 66, find dy/dx by implicit...Ch. 5.5 - Prob. 66ECh. 5.5 - Prob. 67ECh. 5.5 - Prob. 68ECh. 5.5 - Prob. 69ECh. 5.5 - Prob. 70ECh. 5.5 - Prob. 71ECh. 5.5 - Heights of Children For children between the ages...Ch. 5.5 - Average Life Span One reason for the increase in...Ch. 5.5 - Streaming Music Consumers are spending more on...Ch. 5.5 - Depreciation of Equipment For assets such as...Ch. 5.5 - Depreciation Of Equipment Refer to Exercise 75. A...Ch. 5.5 - Population Growth The population of a town t...Ch. 5.5 - Prob. 78ECh. 5.5 - Maximizing Profit The manager of Seko, an...Ch. 5.5 - Lamberts Law Of Absorption Lamberts law of...Ch. 5.5 - Prob. 81ECh. 5.5 - Elasticity of demand a. In Section 3.4, we defined...Ch. 5.5 - Prob. 83ECh. 5.5 - Prob. 84ECh. 5.5 - Prob. 85ECh. 5.5 - Prob. 86ECh. 5.5 - Predator-Prey Model The relationship between the...Ch. 5.5 - Prob. 88ECh. 5.5 - Prob. 89ECh. 5.5 - In Exercises 89 and 90, use the guidelines on page...Ch. 5.5 - Prob. 91ECh. 5.5 - Prob. 92ECh. 5.5 - In Exercises 93-96, use the results of Exercises...Ch. 5.5 - Prob. 94ECh. 5.5 - In Exercises 93-96, use the results of Exercises...Ch. 5.5 - Prob. 96ECh. 5.5 - Prob. 97ECh. 5.5 - Prob. 98ECh. 5.5 - Prob. 99ECh. 5.5 - Use the definition of the derivative to show that...Ch. 5.6 - Give the model for unrestricted exponential growth...Ch. 5.6 - What is the half-life of a radioactive substance?Ch. 5.6 - What is the logistic growth function? What are its...Ch. 5.6 - Exponential Growth Given that a quantity Q(t) is...Ch. 5.6 - Exponential Decay Given that a quantity Q(t)...Ch. 5.6 - Growth Of Bacteria The growth rate of the...Ch. 5.6 - World Population The world population at the...Ch. 5.6 - World Population Refer to Exercise 4. a. If the...Ch. 5.6 - Resale Value Garland Mills purchased a certain...Ch. 5.6 - Atmospheric Pressure If the temperature is...Ch. 5.6 - Radioactive Decay The radioactive element polonium...Ch. 5.6 - Radioactive Decay Phosphorus 32 (P-32) has a...Ch. 5.6 - Nuclear Fallout Strontium 90 (Sr-90), a...Ch. 5.6 - Carbon-14 Dating Wood deposits recovered from an...Ch. 5.6 - Carbon-14 Dating The skeletal remains of the...Ch. 5.6 - Bank Failures In the wake of the 2008 financial...Ch. 5.6 - Prob. 14ECh. 5.6 - Exponential Growth Sales The sales of the Garland...Ch. 5.6 - Learning Curves The American Court Reporting...Ch. 5.6 - Prob. 17ECh. 5.6 - Effect Of Advertising On Sales Metro Department...Ch. 5.6 - Demand For Computers Universal Instruments found...Ch. 5.6 - Reliability of Computer Chips The percentage of a...Ch. 5.6 - Lengths Of Fish The length (in centimeters) of a...Ch. 5.6 - Spread of an Epidemic During a flu epidemic, the...Ch. 5.6 - Growth of a Fruit Fly Population On the basis of...Ch. 5.6 - Demographics The number of citizens aged 45-64...Ch. 5.6 - Prob. 25ECh. 5.6 - Population Growth in the Twenty-First Century The...Ch. 5.6 - Dissemination of Information Three hundred...Ch. 5.6 - Prob. 28ECh. 5.6 - Prob. 29ECh. 5.6 - Von Bertalanffy Growth Function The length (in...Ch. 5.6 - Absorption of Drugs The concentration of a drug in...Ch. 5.6 - Concentration of Glucose in the Bloodstream A...Ch. 5.6 - Radioactive Decay A radioactive substance decays...Ch. 5.6 - Prob. 34ECh. 5.6 - a. Use the results of Exercise 34 to show that the...Ch. 5.6 - Prob. 36ECh. 5.6 - Logistic Growth Function The carrying capacity of...Ch. 5.6 - Gompertz Growth Curve Consider the function Q(t) =...Ch. 5.6 - Air Travel Air travel has been rising dramatically...Ch. 5.6 - Prob. 2TECh. 5.6 - Computer Game Sales The total number of Stan...Ch. 5.6 - Population Growth in the Twenty-First Century The...Ch. 5.6 - Prob. 5TECh. 5.6 - Prob. 6TECh. 5.6 - Absorption of Drugs The concentration of a drug in...Ch. 5.6 - Prob. 8TECh. 5 - The function f(x) = xb (b, a real number) is...Ch. 5 - Prob. 2CRQCh. 5 - Prob. 3CRQCh. 5 - Prob. 4CRQCh. 5 - Prob. 5CRQCh. 5 - Prob. 6CRQCh. 5 - Prob. 7CRQCh. 5 - Prob. 8CRQCh. 5 - a. In the unrestricted exponential growth model Q...Ch. 5 - Prob. 10CRQCh. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - In Exercises 6-8, given that ln 2 = x, ln 3 = y,...Ch. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Prob. 12RECh. 5 - How long will it take for an investment of 10,000...Ch. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 - Prob. 18RECh. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 - Prob. 22RECh. 5 - Prob. 23RECh. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - Prob. 26RECh. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Prob. 29RECh. 5 - Prob. 30RECh. 5 - Prob. 31RECh. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Prob. 34RECh. 5 - Prob. 35RECh. 5 - Prob. 36RECh. 5 - Prob. 37RECh. 5 - Prob. 38RECh. 5 - Prob. 39RECh. 5 - Prob. 40RECh. 5 - Prob. 41RECh. 5 - Prob. 42RECh. 5 - Prob. 43RECh. 5 - Find the absolute extrema of the function...Ch. 5 - Prob. 45RECh. 5 - Prob. 46RECh. 5 - Prob. 47RECh. 5 - Prob. 48RECh. 5 - GROWTH OF Bacteria A culture of bacteria that...Ch. 5 - RADIOACTIVE Decay The radioactive element radium...Ch. 5 - Demand for DVD Players VCA Television found that...Ch. 5 - Radioactivity The mass of a radioactive isotope at...Ch. 5 - Prob. 53RECh. 5 - Prob. 54RECh. 5 - Price of a Commodity The price of a certain...Ch. 5 - FLU EPIDEMIC During a flu epidemic, the number of...Ch. 5 - World Population The world population is projected...Ch. 5 - U.S. INFANT MORTALITY rate The U.S. infant...Ch. 5 - Maximizing Revenue The unit selling price p (in...Ch. 5 - Prob. 60RECh. 5 - Prob. 1BMCh. 5 - Prob. 2BMCh. 5 - Prob. 3BMCh. 5 - Prob. 4BMCh. 5 - Prob. 5BMCh. 5 - Prob. 6BM
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- Grazing Kangaroos The amount of vegetation eaten in a day by a grazing animal V of food available measured as biomass, in units such as pounds per acre. This relationship is called the functional response. If there is little vegetation available, the daily intake will be small, since the animal will have difficulty finding and eating the food. As the amount of food biomass increases, so does the daily intake. Clearly, though, there is a limit to the amount the animal will eat, regardless of the amount of food available. This maximum amount eaten is the satiation level. a.For the western grey kangaroo of Australia, the functional response is G=2.54.8e0.004V, where G=G(V) is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Draw a graph of G against V. Include vegetation biomass levels up to 2000 pounds per acre. ii. Is the graph you found in part i concave up or concave down? Explain in practical terms what your answer means about how this kangaroo feeds. iii. There is a minimal vegetation biomass level below which the western grey kangaroo will eat nothing. Another way of expressing this is to say that the animal cannot reduce the food biomass below this level. Find this minimal level. iv. Find the satiation level for the western grey kangaroo. b. For the red kangaroo of Australia, the functional response is R=1.91.9e0.033V, Where R is the daily intake measured in pounds and V is the vegetation biomass measured in pounds per acre. i. Add the graph of R against V to the graph of G you drew in part a. ii. A simple measure of the grazing efficiency of an animal involves the minimal vegetation biomass level described above: The lower the minimal level for an animal, the more efficient it is at grazing. Which is more efficient at grazing, the western grey kangaroo or the red kangaroo?arrow_forwardSales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s, and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?arrow_forwardWhen a certain drug is taken orally, the concentration of the drug in the patient's bloodstream After t minutes is given by C(t)=0.06t0.0002t2 where 0t240 and concentration is measured in mg/L .When is the maximum serum concentration reached, and what is that maximum concentration?arrow_forward
- Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.arrow_forwardEastern Pacific Yellowfin Tuna Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded N=1481+36e2.61t where t is measured in years and N is measured in thousands of tons of fish. a. What is the r value for the Eastern Pacific yellowfin tuna? b. What is the carrying capacity K for the Eastern Pacific yellowfin tuna? c. What is the optimum yield level? d. Use your calculator to graph N versus t. e. At what time was the population growing the most rapidly?arrow_forwardbThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forward
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